Finite Group Databasebeta

← #10819894

Subgroups — #10819894

Order 768.

1126 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4712C211yesmaximal, characteristic
2C2×#4710C211yesmaximal, characteristic, complemented
3C2×C4×D24C211yesmaximal, characteristic, complemented
4#73655C211yesmaximal, characteristic, complemented
5#73653C211yesmaximal, characteristic, complemented
6C3×#1771C211yesmaximal, characteristic, complemented
7#70458C211yesmaximal, characteristic, complemented
8#70457C211yesmaximal, characteristic, complemented
9#69825C211yesmaximal, characteristic, complemented
10#69814C211yesmaximal, characteristic, complemented
11#69774C211yesmaximal, characteristic, complemented
12#68686C211yesmaximal, characteristic, complemented
13#68673C211yesmaximal, characteristic, complemented
14#68673C211yesmaximal, characteristic, complemented
15#68672C211yesmaximal, characteristic, complemented
16#23195—31nomaximal, Sylow
17C22×D24C2211yescharacteristic
18C22×D24C2211yescharacteristic
19C22×#204C2211yescharacteristic
20C22×#204C2211yescharacteristic
21C2×#893—21no—
22C2×#875C2211yescharacteristic
23C2×#874C2211yescharacteristic
24C2×C4×D12C2211yescharacteristic
25C2×C4×D12C2211yescharacteristic
26C2×C4×D12C2211yescharacteristic
27C2×C4×Dic6C2211yescharacteristic
28C2×C3×C4⋊C8C2211yescharacteristic
29C2×C3×#97C2211yescharacteristic
30C2×C3×#97C2211yescharacteristic
31C2×C3×C4×C8C2211yescharacteristic
32C3×C4×C4⋊C4C2211yescharacteristic
33C2×#821C2211yescharacteristic
34C2×#821C2211yescharacteristic
35C2×#821C2211yescharacteristic
36C2×#821C2211yescharacteristic
37C2×#821C2211yescharacteristic
38C2×#821C2211yescharacteristic
39C2×#818C2211yescharacteristic
40C2×#817C2211yescharacteristic
41C2×#816C2211yescharacteristic
42C2×#816C2211yescharacteristic
43#4990—21no—
44#4989—21no—
45#4988—21no—
46#4939C2211yescharacteristic
47#4939C2211yescharacteristic
48#4939C2211yescharacteristic
49C4×C4⋊Dic3C2211yescharacteristic
50C4×C4⋊Dic3C2211yescharacteristic
51#4929C2211yescharacteristic
52#4712C418yescomplemented
53#4710—24no—
54C4×D24—24no—
55#4669—21no—
56#4666—21no—
57#4665—21no—
58#4665—21no—
59C3×#336C2211yescharacteristic
60C3×#336C2211yescharacteristic
61#4551C2211yescharacteristic
62#4551C2211yescharacteristic
63C2×#496—31no—
64C2×#440—31no—
65C2×C4×D8—31no—
66#2367—31no—
67#2366—31no—
68#1983—31no—
69#1982—31no—
70#1972—31no—
71#1968—31no—
72#1880—31no—
73#1879—31no—
74#1879—31no—
75#1877—31no—
76#1776—31no—
77#1771D311yescharacteristic, complemented
78C22×D12—21no—
79C22×D12—21no—
80C22×D12C2311yescharacteristic
81C22×D12C2311yescharacteristic
82C22×D12C2311yescharacteristic
83C22×C4×D3—21no—
84C22×C4×D3—21no—
85C22×C4×D3—21no—
86C22×Dic6C2311yescharacteristic
87C22×C3×C8C2311yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C22×C3×C8C2311yescharacteristic
91C2×C3×C4⋊C4D411yescharacteristic
92C2×C3×C4⋊C4D411yescharacteristic
93C2×C3×C42C2311yescharacteristic
94C2×C3×C42C2311yescharacteristic
95C2×C3×C42C2311yescharacteristic
96C2×(C2×D3)⋊C4—21no—
97C2×(C2×D3)⋊C4—21no—
98C2×(C2×D3)⋊C4—21no—
99C2×(C2×D3)⋊C4—21no—
100C2×(C2×D3)⋊C4—21no—
101C2×(C2×D3)⋊C4—21no—
102C2×(C2×D3)⋊C4—21no—
103C2×(C2×D3)⋊C4—21no—
104C2×(C2×D3)⋊C4—21no—
105C2×(C2×D3)⋊C4—21no—
106C2×(C2×D3)⋊C4—21no—
107C2×C4⋊Dic3C2311yescharacteristic
108C2×C4⋊Dic3C2311yescharacteristic
109C2×C4⋊Dic3C2311yescharacteristic
110C2×C4⋊Dic3C2311yescharacteristic
111C2×Dic3⋊C4—21no—
112C2×C4×Dic3—21no—
113C2×C4×Dic3—21no—
114C2×C4×Dic3—21no—
115C2×D24—22no—
116C2×D24—22no—
117C2×D24—41no—
118C2×D24—41no—
119C2×D24C2×C414yescomplemented
120C2×D24C2×C414yescomplemented
121C2×#204—22no—
122C2×#204—22no—
123C2×#204—41no—
124C2×#204—41no—
125C2×#204C2×C414yescomplemented
126C2×#204C2×C414yescomplemented
127#893—44no—
128#875—22no—
129#875C2×C414yescomplemented
130#874—22no—
131#874C2×C414yescomplemented
132C4×D12—22no—
133C4×D12—22no—
134C4×D12—22no—
135C4×D12—41no—
136C4×D12—41no—
137C4×D12—41no—
138C4×Dic6—22no—
139C4×Dic6—41no—
140C3×C4⋊C8—22no—
141C3×#97—22no—
142C3×#97C2×C414yescomplemented
143C3×C4×C8—22no—
144C3×#95D411yescharacteristic
145C3×#95D411yescharacteristic
146C3⋊#95—21no—
147C3⋊#95—21no—
148C3⋊#95—21no—
149C3⋊#95—21no—
150#821—22no—
151#821—22no—
152#821—22no—
153#821—41no—
154#821—41no—
155#821—41no—
156#818D414yescomplemented
157#817—22no—
158#816—22no—
159#816—41no—
160C22×SD16—31no—
161C22×SD16—31no—
162C22×D8—31no—
163C22×D8—31no—
164C2×#127—31no—
165C2×#124—31no—
166C2×C4×Q8—31no—
167C2×C4×D4—31no—
168C2×C4×D4—31no—
169C2×C4×D4—31no—
170C2×C4×D4—61no—
171#496—38no—
172#440—64no—
173C4×D8—64no—
174C2×#107—31no—
175C2×#106—31no—
176C2×C4⋊C8C2×D311yescharacteristic
177C2×#103—31no—
178C2×#103—31no—
179C2×#102—31no—
180C2×#102—31no—
181C2×#102—31no—
182C2×#102—31no—
183C2×#102—31no—
184C2×#102—31no—
185C2×#97C2×D311yescharacteristic
186C2×#97C2×D311yescharacteristic
187C2×C4×C8C2×D311yescharacteristic
188#391—31no—
189#390—31no—
190#390—31no—
191#390—31no—
192#390—61no—
193#388—61no—
194#388—61no—
195#386—61no—
196#386—61no—
197#385—61no—
198C4×C4⋊C4—31no—
199C4×C4⋊C4—31no—
200C4×C4⋊C4C2×D311yescharacteristic
201C4×C22⋊C4—61no—
202#340—31no—
203#340—31no—
204#336C2×D311yescharacteristic
205#336C2×D311yescharacteristic
206C23×D3—21no—
207C23×D3—21no—
208C23×D3—21no—
209C22×C3×C4C2×D411yescharacteristic
210C22×C3×C4C2×D411yescharacteristic
211C22×C3×C4C2×D411yescharacteristic
212C22×C3×C4C2×D411yescharacteristic
213C22×C3×C4C2×D411yescharacteristic
214C22×C3×C4C2×D411yescharacteristic
215C22×C3×C4C2411yescharacteristic
216C22×Dic3—21no—
217C22×Dic3—21no—
218C22×Dic3—21no—
219C22×Dic3—21no—
220C22×Dic3—21no—
221C2×D12—21no—
222C2×D12—21no—
223C2×D12—21no—
224C2×D12—21no—
225C2×D12—21no—
226C2×D12—21no—
227C2×D12—21no—
228C2×D12—21no—
229C2×D12—21no—
230C2×D12—21no—
231C2×D12—21no—
232C2×D12—21no—
233C2×D12—24no—
234C2×D12—21no—
235C2×D12—21no—
236C2×D12—21no—
237C2×D12—24no—
238C2×D12—42no—
239C2×D12—42no—
240C2×D12—81no—
241C2×D12—81no—
242C2×D12C22×C412yes—
243C2×D12C22×C412yes—
244C2×D12C22×C412yes—
245C2×C4×D3—42no—
246C2×C4×D3—42no—
247C2×C4×D3—42no—
248C2×C4×D3—42no—
249C2×C4×D3—42no—
250C2×C4×D3—42no—
251C2×C4×D3—81no—
252C2×C4×D3—81no—
253C2×C4×D3—81no—
254C2×Dic6—21no—
255C2×Dic6—21no—
256C2×Dic6—21no—
257C2×Dic6—21no—
258C2×Dic6—21no—
259C2×Dic6C22×C412yes—
260C2×C3×C8—21no—
261C2×C3×C8—21no—
262C2×C3×C8—21no—
263C2×C3×C8—21no—
264C2×C3×C8—21no—
265C2×C3×C8—21no—
266C2×C3×C8—21no—
267C2×C3×C8—21no—
268C2×C3×C8C22×C412yes—
269C2×C3×C8C22×C412yes—
270C2×C3×C8C2×D412yes—
271C2×C3×C8#4112yes—
272C3×C4⋊C4—22no—
273C3×C4⋊C4—41no—
274C3×C42—21no—
275C3×C42—21no—
276C3×C42—21no—
277C3×C42—21no—
278C3×C42C22×C412yes—
279C3×C42#4112yes—
280(C2×D3)⋊C4—24no—
281(C2×D3)⋊C4—24no—
282(C2×D3)⋊C4—42no—
283(C2×D3)⋊C4—42no—
284(C2×D3)⋊C4—42no—
285(C2×D3)⋊C4—42no—
286(C2×D3)⋊C4—42no—
287(C2×D3)⋊C4—42no—
288(C2×D3)⋊C4—81no—
289(C2×D3)⋊C4—81no—
290(C2×D3)⋊C4—81no—
291C4⋊Dic3—21no—
292C4⋊Dic3—21no—
293C4⋊Dic3—21no—
294C4⋊Dic3—21no—
295C4⋊Dic3—21no—
296C4⋊Dic3—21no—
297C4⋊Dic3C2×D412yes—
298C4⋊Dic3C2×D412yes—
299Dic3⋊C4—42no—
300C4×Dic3—42no—
301C4×Dic3—42no—
302C4×Dic3—81no—
303D24—28no—
304D24—44no—
305#204—28no—
306#204—44no—
307C22×Q8—31no—
308C22×D4—31no—
309C22×D4—31no—
310C22×D4—31no—
311C22×D4—61no—
312C22×D4—61no—
313C23×C4—61no—
314C23×C4—61no—
315C23×C4—61no—
316C2×SD16—34no—
317C2×SD16—34no—
318C2×SD16—62no—
319C2×SD16—62no—
320C2×SD16—121no—
321C2×SD16—121no—
322C2×D8—34no—
323C2×D8—34no—
324C2×D8—62no—
325C2×D8—62no—
326C2×D8—121no—
327C2×D8—121no—
328C22×C8C22×D311yescharacteristic
329C22×C8C22×D311yescharacteristic
330C22×C8C22×D311yescharacteristic
331C22×C8C22×D311yescharacteristic
332#127—34no—
333#127—62no—
334#124—34no—
335#124—62no—
336C4×Q8—62no—
337C4×Q8—121no—
338C4×D4—62no—
339C4×D4—62no—
340C4×D4—62no—
341C4×D4—121no—
342C4×D4—121no—
343C4×D4—121no—
344C4×D4—124no—
345C2×C4⋊C4—31no—
346C2×C4⋊C4—31no—
347C2×C4⋊C4—31no—
348C2×C4⋊C4—31no—
349C2×C4⋊C4—61no—
350C2×C4⋊C4D1211yescharacteristic
351C2×C4⋊C4D1211yescharacteristic
352C2×C22⋊C4—61no—
353C2×C22⋊C4—61no—
354C2×C22⋊C4—61no—
355C2×C22⋊C4—61no—
356C2×C22⋊C4—61no—
357C2×C22⋊C4—61no—
358C2×C22⋊C4—61no—
359C2×C22⋊C4—61no—
360C2×C22⋊C4—61no—
361C2×C22⋊C4—61no—
362C2×C22⋊C4—61no—
363C2×C42—61no—
364C2×C42—61no—
365C2×C42—61no—
366C2×C42C22×D311yescharacteristic
367C2×C42C22×D311yescharacteristic
368C2×C42C22×D311yescharacteristic
369#107—34no—
370#106—62no—
371C4⋊C8—22no—
372#103—62no—
373#103—121no—
374#102—62no—
375#102—62no—
376#102—62no—
377#102—121no—
378#102—121no—
379#102—121no—
380#97—22no—
381#97C4×D314yescomplemented
382C4×C8—22no—
383#95—61no—
384#95—61no—
385#95—61no—
386#95—61no—
387#95D1211yescharacteristic
388#95D1211yescharacteristic
389C23×C3C22×D411yescharacteristic
390C22×D3—22no—
391C22×D3—22no—
392C22×D3—22no—
393C22×D3—41no—
394C22×D3—41no—
395C22×D3—41no—
396C22×D3—41no—
397C22×D3—41no—
398C22×D3—41no—
399C22×D3—41no—
400C22×D3—41no—
401C22×D3—41no—
402C22×D3—41no—
403C22×D3—41no—
404C22×D3—41no—
405C22×D3—41no—
406C22×D3—41no—
407C22×D3—41no—
408C22×D3—41no—
409C22×D3—41no—
410C22×D3—41no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4C4×D412yes—
427C2×C3×C4C4×D412yes—
428C2×C3×C4AGL(1,ℤ/8)12yes—
429C2×C3×C4C23×C411yescharacteristic
430C2×C3×C4C22×D411yescharacteristic
431C2×C3×C4C2×#4111yescharacteristic
432C2×C3×C4C2×#4111yescharacteristic
433C2×C3×C4H(5,𝔽2)11yescharacteristic
434C2×C3×C4H(5,𝔽2)11yescharacteristic
435C2×Dic3—22no—
436C2×Dic3—22no—
437C2×Dic3—22no—
438C2×Dic3—41no—
439C2×Dic3—41no—
440C2×Dic3—41no—
441C2×Dic3—41no—
442C2×Dic3—41no—
443C2×Dic3—41no—
444C2×Dic3—41no—
445C2×Dic3—41no—
446C2×Dic3—41no—
447C2×Dic3—41no—
448C2×Dic3—41no—
449C2×Dic3—41no—
450D12—22no—
451D12—22no—
452D12—22no—
453D12—22no—
454D12—22no—
455D12—22no—
456D12—48no—
457D12—41no—
458D12—41no—
459D12—41no—
460D12—41no—
461D12—41no—
462D12—41no—
463D12—84no—
464C4×D3—84no—
465C4×D3—84no—
466C4×D3—84no—
467Dic6—22no—
468Dic6—22no—
469Dic6—41no—
470Dic6—41no—
471C3×C8—22no—
472C3×C8—41no—
473C3×C8—41no—
474C3×C8C4×D414yescomplemented
475C24—61no—
476C24—61no—
477C24—61no—
478C2×Q8—32no—
479C2×Q8—61no—
480C2×Q8—61no—
481C2×Q8—61no—
482C2×Q8—61no—
483C2×Q8—61no—
484C2×D4—32no—
485C2×D4—32no—
486C2×D4—32no—
487C2×D4—64no—
488C2×D4—64no—
489C2×D4—61no—
490C2×D4—61no—
491C2×D4—61no—
492C2×D4—61no—
493C2×D4—61no—
494C2×D4—61no—
495C2×D4—61no—
496C2×D4—61no—
497C2×D4—61no—
498C2×D4—61no—
499C2×D4—61no—
500C2×D4—61no—
501C2×D4—61no—
502C2×D4—61no—
503C2×D4—61no—
504C2×D4—122no—
505C2×D4—122no—
506C2×D4—241no—
507C2×D4—241no—
508C22×C4—61no—
509C22×C4—61no—
510C22×C4—61no—
511C22×C4—61no—
512C22×C4—61no—
513C22×C4—122no—
514C22×C4—122no—
515C22×C4—122no—
516C22×C4—122no—
517C22×C4—122no—
518C22×C4—122no—
519C22×C4—241no—
520C22×C4—241no—
521C22×C4—241no—
522C22×C4C2×D1211yescharacteristic
523C22×C4C2×D1211yescharacteristic
524C22×C4C2×D1211yescharacteristic
525C22×C4C2×D1211yescharacteristic
526C22×C4C2×D1211yescharacteristic
527C22×C4C2×D1211yescharacteristic
528C22×C4C23×D311yescharacteristic
529SD16—68no—
530SD16—124no—
531D8—68no—
532D8—124no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8C2×C4×D312yes—
542C2×C8C2×C4×D312yes—
543C2×C8D3×D412yes—
544C2×C8#23912yes—
545C4⋊C4—22no—
546C4⋊C4—32no—
547C4⋊C4—32no—
548C4⋊C4—41no—
549C4⋊C4—61no—
550C4⋊C4—61no—
551C4⋊C4—61no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—61no—
555C4⋊C4—122no—
556C22⋊C4—64no—
557C22⋊C4—64no—
558C22⋊C4—122no—
559C22⋊C4—122no—
560C22⋊C4—122no—
561C22⋊C4—122no—
562C22⋊C4—122no—
563C22⋊C4—122no—
564C22⋊C4—241no—
565C22⋊C4—241no—
566C22⋊C4—241no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—21no—
571C42—122no—
572C42—122no—
573C42—241no—
574C42C2×C4×D312yes—
575C42#23512yes—
576C22×C3C2×C4×D411yescharacteristic
577C22×C3D4211yescharacteristic
578C22×C3#55011yescharacteristic
579C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
580C22×C3#57511yescharacteristic
581C22×C3#57611yescharacteristic
582C22×C3#57711yescharacteristic
583C2×D3—42no—
584C2×D3—42no—
585C2×D3—42no—
586C2×D3—42no—
587C2×D3—42no—
588C2×D3—42no—
589C2×D3—42no—
590C2×D3—42no—
591C2×D3—42no—
592C2×D3—81no—
593C2×D3—81no—
594C2×D3—81no—
595C2×D3—81no—
596C2×D3—81no—
597C2×D3—81no—
598C2×D3—81no—
599C2×D3—81no—
600C2×D3—81no—
601C2×D3—81no—
602C2×D3—81no—
603C2×D3—81no—
604C3×C4—22no—
605C3×C4—22no—
606C3×C4—22no—
607C3×C4—41no—
608C3×C4—41no—
609C3×C4—41no—
610C3×C4C2×C4×D411yescharacteristic
611C3×C4#51811yescharacteristic
612C3×C4#55011yescharacteristic
613C3×C4#55911yescharacteristic
614Dic3—42no—
615Dic3—42no—
616Dic3—42no—
617Dic3—81no—
618Dic3—81no—
619C23—62no—
620C23—62no—
621C23—62no—
622C23—121no—
623C23—121no—
624C23—121no—
625C23—121no—
626C23—121no—
627C23—121no—
628C23—121no—
629C23—121no—
630C23—121no—
631C23—121no—
632C23—121no—
633C23—121no—
634C23—121no—
635C23—121no—
636C23—121no—
637C23—121no—
638C23—121no—
639C23—121no—
640C23C22×D1211yescharacteristic
641Q8—62no—
642Q8—62no—
643Q8—121no—
644Q8—121no—
645D4—62no—
646D4—62no—
647D4—62no—
648D4—62no—
649D4—62no—
650D4—62no—
651D4—128no—
652D4—121no—
653D4—121no—
654D4—121no—
655D4—121no—
656D4—121no—
657D4—121no—
658D4—244no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—62no—
675C2×C4—62no—
676C2×C4—62no—
677C2×C4—121no—
678C2×C4—121no—
679C2×C4—121no—
680C2×C4—121no—
681C2×C4—121no—
682C2×C4—121no—
683C2×C4—121no—
684C2×C4—121no—
685C2×C4—121no—
686C2×C4—121no—
687C2×C4—121no—
688C2×C4—121no—
689C2×C4—244no—
690C2×C4—244no—
691C2×C4—244no—
692C2×C4C4×D1212yes—
693C2×C4C4×D1212yes—
694C2×C4#90812yes—
695C2×C4C22×C4×D311yescharacteristic
696C2×C4C2×#23511yescharacteristic
697C2×C4C2×D3×D411yescharacteristic
698C2×C4C2×#23911yescharacteristic
699C2×C4#100911yescharacteristic
700C2×C4#100911yescharacteristic
701C8—22no—
702C8—41no—
703C8—41no—
704C8#89314yescomplemented
705C2×C3#236611yescharacteristic
706C2×C3C4×AGL(1,ℤ/8)11yescharacteristic
707C2×C3#294611yescharacteristic
708C2×C3#326411yescharacteristic
709C2×C3#327111yescharacteristic
710C2×C3#339711yescharacteristic
711C2×C3#340311yescharacteristic
712D3—82no—
713D3—82no—
714D3—82no—
715C22—122no—
716C22—122no—
717C22—122no—
718C22—122no—
719C22—122no—
720C22—122no—
721C22—122no—
722C22—122no—
723C22—122no—
724C22—241no—
725C22—241no—
726C22—241no—
727C22—241no—
728C22—241no—
729C22—241no—
730C22—241no—
731C22—241no—
732C22—241no—
733C22—241no—
734C22—241no—
735C22—241no—
736C22C2×C4×D1211yescharacteristic
737C22D4×D1211yescharacteristic
738C22#557711yescharacteristic
739C22C2×#90811yescharacteristic
740C22#574811yescharacteristic
741C22#575111yescharacteristic
742C22#575211yescharacteristic
743C4—22no—
744C4—22no—
745C4—22no—
746C4—41no—
747C4—41no—
748C4—41no—
749C4—122no—
750C4—122no—
751C4—122no—
752C4—241no—
753C4—241no—
754C4C2×#89311yescharacteristic
755C4#552111yescharacteristic
756C4#555311yescharacteristic
757C4#558511yescharacteristic
758C3#2319511yescharacteristic, complemented, Sylow
759C2—242no—
760C2—242no—
761C2—242no—
762C2#7365311yescharacteristic
763C2C4×#90811yescharacteristic
764C2#7856011yescharacteristic
765C2#7949311yescharacteristic
766C2#7950811yescharacteristic
767C2#7995011yescharacteristic
768C2#7995611yescharacteristic
subgroupG/H
centerC23C22×D12
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1771C2
socleC23×C3C22×D4
prime radicalC2×#4712C2
cosocleC22×C3×C4C24
hypercenter#1771D3
hypocenterC3#23195
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1771

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#4710C2semidirect
3. C2×C4×D24C2semidirect
4. #73655C2semidirect
5. #73653C2semidirect
6. C3×#1771C2semidirect
7. #70458C2semidirect
8. #70457C2semidirect
9. #69825C2semidirect
10. #69814C2semidirect
11. #69774C2semidirect
12. #68686C2semidirect
13. #68673C2semidirect
14. #68673C2semidirect
15. #68672C2semidirect
52. #4712C4semidirect
77. #1771D3semidirect
119. C2×D24C2×C4semidirect
120. C2×D24C2×C4semidirect
125. C2×#204C2×C4semidirect
126. C2×#204C2×C4semidirect
129. #875C2×C4semidirect
131. #874C2×C4semidirect
142. C3×#97C2×C4semidirect
156. #818D4semidirect
381. #97C4×D3semidirect
474. C3×C8C4×D4semidirect
704. C8#893semidirect
758. C3#23195semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#47122
C2×#47102
C2×C4×D242
#736552
#736532
C3×#17712
#704582
#704572
#698252
#698142
#697742
#686862
#686732
#686722
#231953